1327
Ana/. Chem. 1983, 55, 827-832
Double-Comparison Method for Mass Spectrometric Determination of Hydrogen Isotopic Abundances D. A. Schoeller,' D. W. Peterson,2 and J. M. Hayes" Biogeochemical Laboratories, Departments af Chemistry and of Geologyr Indiana University, Bloomington, Indiana 4 7405
Hydrogen lsotopa ratio analysis Is subject to Interference from H,', and the unoertalnty In the H,' correctlon Is generally the llmltlng factor In the preclslon of hydrogen lsotoplc analyses. Mathematlcal niodellng lndlcates that the preclslon of the analysls can be Improved through the use of a double-comparlson technlque employlng a second reference gas. I n order to compare the slngle- and double-comparison technlques, a double-collector Isotope ratlo mass spectrometer was fltted wlth a triple VISCOUS leak Inlet system. Four H2 samples wlth douterlum contents between -184 and 193% vs. standard mean ocean water were analyzed by both techniques. Tho single-comparlson analyses had a preclslon of about l % o . The double-comparlson analysis had a preclslon of 0.4%0 when comblned wlth electrical H,' correctlon. When no H,' correctlon was used In the double-comparlson measurements, the preclslon varled as a function of degree of mlsmatchlng of major Ion currents of the unknown and reference gaserr and was frequently as poor as 5%0.
Measurements of the relative abundances of the stable isotopes of hydrogen are based on the methodology of differential isotope ratio mass spectrometry that was developed by Nier ( I ) and by McKinney et al. (2). In the particular case of hydrogen, however, the measurement is subject to errors due to ion-molecule reactions in the ion source. The product of these reactions, H3+,has the same nominal mass as the minor isotopic species HD+ (where D designates 2H), Thus, the observed ion-current ratio of mass 3 to mass 2 depends not only on the isotope ratio but also on the extent of this ion-molecule reaction. The H3+contribution can be reduced by operating at low Hz pressure in the ion source (in order to decrease the frequency of H2-Hz+collisions) and/or at high accelerating or repeller voltages (in order to decrease the residence time of Hz+in the ion source), but even under these conditions H3+constitutes 5-30% of the mass 3 ion current (3, 4 ) . Accurate determinations, therefore, must include a correction for the presence of the HS+. The precision of that correction has a significant effect on the overall precision of the measurement. To understand the formation of H3+, and, in that way, strategies for correcting the ion current ratio measurement, note that the reaction producing this species is
Hz
+ Hz+
H3+
+ H-
(1)
Because the abundance of H2+is directly proportional to the is dependent on partial pressure of Hz, the abundance of H3+ the square of the H2pressure. Thus, if the expression for the ratio of mass 2 and 3 ion currents (2) YZ = i 3 J i 2 = (iHD iHs)/iH,
+
is rewritten in terms of the abundances of neutral molecules Permanent address: Department of Medicine, University of Chicago, Chicago, IL 60637. Present address: Scientific Instruments Division, HewlettPackard, Palo Alto, CA 94304.
in the ion source, the following is obtained:
where K is a constant proportional to the rate of H3+formation (eq 1). Equation 3 is of the form y = a bx, and regressiion of the observed ion-current ratio on sample pressure (Le., [H[,]) will yield the true isotope ratio as the a term, or intercept, and K as the b term, or slope. Because the regression procedure is time-consuming and laborious, it is not routinely used. Rather, one of two alternatives is chosen. The first, a purely mathematical correction (3,5), can be used by defining K in terms of the mass 2 ion current and correcting each observed ion current ratio
+
where i2is the precise mass 2 ion current in the observations to be corrected. The other method, an electrical correction ( 4 ) that is theoretically superior in coping with short-term fluctuation in sample pressure, involves the analog subtraction of iHBfrom i3
iHD= i3 - iHs= i3 - K(iH,)'
((5)
In practice, this can be accomplished by squaring the miass 2 signal and subtracting a fraction of the result from the mass 3 signal. The value of K in eq 5 is thus represented by the setting of a voltage-dividing potentiometer that is simply adjusted until the observed ratio of signals is independent of sample pressure. In either of these approaches, a calibration or "set-up" run is used to correct measurements made at some other time. In this case, drifts in instrumental conditions can have severe effects that may be undetected if standard samples are riot checked very frequently. Hydrogen isotope ratio measusements are, thus, subject to l/f noise in a way that is very different from isotope ratio measurements of carbon, nitrogen, and oxygen. While a single-comparison method of measurement has yielded remarkable performance for those elements, some more elaborate scheme may be helpful for hydrogen. A double-comparison method of correcting for the H3+ contribution that may reduce the sensitivity to l/f noise has been proposed by Terwilliger (6). This approach involves the use of two reference gases that are analyzed in sequence wrth the unknown. The advantage of using a second reference gas has long been recognized (7), and parallel strategies of measurement have been employed for other elements (8), but the actual use of a triple inlet system employing the method for hydrogen has not been described. In this report, a triple inlet mass spectrometer for performing double-comparison hydrogen isotope ratio measuirements is described. In addition, mathematical models of the single- and double-comparison methods have been developed for the purpose of determining the theoretical precision and optimal conditions. The precision of the double-comparison method has been determined in practice and compared with that of single-comparison methods.
0003-2700/83/0355-0827$01.50/00 1983 American Chemical Society
828
ANALYTICAL CHEMISTRY, VOL. 55, NO. 6, MAY 1983
Table I. Definitions of Symbols and Values of Instrumental Parameters A , B, U d
e
F 2 i.2 13
in
Ai k K n R R' At
t T Vfs un ti SMOW 0
sz
Absolute deuterium abundances for reference gases A and B and unknown gas U. Equations in which these terms appear have the same form (without approximations) for abundances expressed as the ratios HD/H,, H/D, or in the ti notation Vf$FAt, signal change corresponding to the smallest change in the digitizer output, V electronic charge, 1.6 X C maximum output frequency of voltage to frequency converter, l o 5 Hz ion current ion current at mass 2, 1 . 5 X lo-' A ion current at mass 3, [ 6 . 0 X + (4.7 X 1O-l6)6SMOW]A amplifier current noise, A difference between major ion currents of two gases Boltzmann's constant, 1.38 X (V C)/K H; formation constant, 60000/A number of analog to digital conversion, 100 for 100-s observations ratio of minor to major ion currents, subscripts A, B, and U refer to reference as A and B, and unknown, respectively R corrected for H,' integration time for a single analog to digital conversion, 1 s time of integration, 100 s temperzture, 298 K full-scale voltage of voltage to frequency converter, 10 V amplifier voltage noise, V isotopic composition relative to standard mean ocean water, ( D / H ) s ~ o w = 155.76 X (9) standard deviation, subscripts indicate the parameter in question resistance, 1 x 10'" R and 5 X 10" 0 for mass 2 and 3, respectively
-
THEORY
Table 11. Characteristics of Signals and Noise Components
The models for calculating the theoretical precision of the differential hydrogen isotope ratio determination can be developed under three sets of conditions: single-comparison with no H3+ contribution, single comparison with a 30% H3+ contribution, and double-comparison. All results are ultimately presented in terms of the parameter conventionally employed in isotopic analyses
Signal mass
ion current, A
2 H,:
1.5 x 10-9
-
6 = 103[(~;/~2) 11
(7)
where the subscripts refer to an arbitrary isotopic standard,
A, and to an unknown material, U. Single Comparison without H3+. In the absence of any H3+contribution, the variance of the isotope ratio determi-
3b
HD',
4.6 x 10-13
2.7 x 10-13
H,C 1.3 , x 1043 H: 1.3 , x 10-13
Noise
' I
A shorthand notation will be employed in this report. Used without a subscript, 6 refers to measurements in which the isotopic standard designated A serves as the reference point. Abundances referred to the primary isotopic standard, Standard Mean Ocean Water (9),will be designated by &Mow. Because molecular hydrogen is diatomic, the ratio of ion currents is twice as large as the isotope ratio [Le., (i3/i2) (HD/Hz)= 2(D/H)], but cancellation of the factor, 2, allows 6 to be written directly in terms of the ratio of ion currents
3a
HD+,
shot, A electrometer, A digitization, A total, A
1 . 6 x 10-1s 1.3 X lo-'' 2.9 X lo-'' 1.6 x 10-15
3.1 x 10-17 7.2 X 5.7 X lo-'* 7.8 x 10-17
2.6.x 10-17 7.2 X 5.7 X lo-'* 7.7 x 10-17
7.6 x 103
5.2 x 103
S/N 9.6 x 105
-
,-.
Corresponds to sample with t i s ~0 O~ /OO. ~ responds to sample with SSMOW -428 O / O O . a
Cor-
In practice, each ion current is converted to a voltage and digitized. Thus, the variances of the signals corresponding to iz and i3 are influenced by ion-beam shot noise, signalconditioning noise, and digitization noise. The expressions for these noise sources have been derived previously (11) and are summarized below:
nation is controlled by the uncertainty of the ion current measurements (IO)
The variance of the ratio of ion currents (R) is given by
where i2 and i3 are the ion currents at mass 2 and mass 3 , respectively. Evaluation of the derivatives in eq 9 yields
The major terms of eq 11 correspond to shot noise, signal conditioning noise, and digitization noise, respectively. The symbols are defined in Table I. The numerical solution to eq 11 under typical operating conditions for the Indiana University mass spectrometer system (Table I) indicates (Table 11) that the predominant noise source is signal-conditioning noise due to the electrometer for mass 3 and shot noise for mass 2. Substitution of these values into eq 10 indicates that the variance of R is independent of the deuterium abundance because the precision is limited by noise originating in the minor-beam electrometer. are essentially equal and Thus, the variances uRAZand qu2 can be represented by the more general term uRz. Making this substitution in eq 8 and evaluating the dervatives yield
ANALYTICAL CHEMISTRY, VOL. 55, NO. 6, MAY 1983
us2 = 106UR'
(;A
" I
I
;U)
The theoretical precision of the single-comparison isotope ratio determination can be calculated for any pair of hydrogen samples by using eq 12. The results describe the maximum performance obtainable under these instrumental conditions, that is, the precision to be expected if the H3+correction could be made perfectly, with no additional contribution to the overall uncertainty of the measurement. For two samples with the precision of the deisotope ratios similar to SMOW (9)) termination would be 0.19%0. If the unknown were a D-depleted sample such as Standard Light Antarctic Precipitation (SLAP, := -428%0, ref 9), the precision of the determination would be 0 . 2 5 % ~ ~ Single Comparison with H3+Correction. Correction for the H3+interference introduces three additional parameters to the expression for the isotope ratio
RU - KiU
6 = 103( RA - KiA - 1 )
It is useful to recast the ion currents in terms of a base value, I , and to let iA = I and iu = I + A, This allows separate consideration of fluctuations in the hydrogen pressure in the ion source (that is, fluctuations in I due to sources other than ion-beam shot noise) and of mismatches of ion-source pressures between reference and unknown samples. Making these substitutions, we obtain
6 = 103
c
-+ -
RU - K ( I + A) RA - K I
Quantitating the effect of uncertainties in K and the effect of A is straightforward in terms of the propagation of errors. Another approach is required to elucidate the effects of variations in I. These problems will be discussed in sequence. If A and Z are constant, the variance in 6 will be given by
I
R
I
uK= 6000 amp-' (IO
5 '-
%h,
I
1929
I
4. 0
z-
3 '
b"
2.
0' -500
I
-400
I
I
I
I
-300
-200
-100
0
8, %e Flgure 1. Precision of the single-comparison hydrogen isotope analysis. The standard deviation Is plotted as a function of the isotope ratio of the unknown vs. reference A for various levels of uncertainty in the H,+ correction. The values were calculated by using eq 16 and the typical operating conditions are listed in Table I .
amounting to %.9%0(independent of S) for each percentage point of mismatching. On the other hand, if the ion current mismatch is taken into account during H3+ correction, the effect on u6 is very small. For example, if the ion currents are mismatched by 1%, the increase in u6 is 0.04%0for 6 = -5100 and uK = 600 A-l ( l % ) , Consideration of variations in I is particularly relevant because the mathematical correction embodies an assumption that the ion currents are perfectly constant (apart from s tatistical variations described by eq 11)over each data-acquisition interval, M condition which may not always be met. Tlhis requirement of constancy arises in the following way: A1though we have written simply that R' = R - Ki2 (eq 4)) it should be recalled that this relationship derives from a MCond-order dependence of i3on iz, namely, i3 = R'iz + Ki;. If i2 is, in fact, variable over time, the most accurate formulation of the ion-current ratio observed in a data-acquisition interval, t , will be given by
This expression differs from eq 8 by the addition of a term representing uncertainties in the value of K. Evaluation of the derivatives in eq 15 yields
Figure 1 presents results of numerical solutions (conditions given in Table I) of eq 16 for different values of 6 and If there are any uncertainties in K , u6 is dependent on the difference between the isotopic compositions of the sample and reference. The distribution in q values is approximately symmetrical about 6 = 0 (RA = RU). Only one side of the distribution is shiown. It can be seen that,, if the uncertainty in K is greater than 0.1%, the overall precision of the isotope-ratio measurement is limited by the precision of the H3+ correction. (Note: the observed precision of repeated isotope ratio measurements may be much better than the values indicated here. The overall precision, however, must be evaluated not only by repeated measurements of R but also by repeated measurements of K.) If the ion currents are mismatched (A # 0) and wrongly assumed to be equal (A = 0), systematic errors will arise. For the conditions summarized in Table I, the errors are large,
where i&) and iz(t)are the mass 3 and mass 2 ion currents as functions of time. Application of eq 4 (i.e., a linear correction) to a time-averaged ion-current ratio will undercoincontributions generated while i2 was above pensate for H3+ its average value and will overcompensate for those generatled while iz was below its average value. If the fractional deviation of i2about its central value is designated by e, it can be shovvn that, in the presence of this variation, the exact relationship between R and R' is different from eq 4 and is given by
R' = R
- K&(l
+ e2)
(18)
The absence of terms carrying E to the first power is notable and minimizes the errors associated with use of the inexact linear correction. Further, if both reference and unknown ion currents are equally unstable, inexact corrections for H3+in the opposing observations will approximately cancel during the calculation of 6 values. If, for example, 6sMowA = 0, GSMOWU = -500, and e = 0.03 for both samples (i.e., both ion currents vary &3% from their mean values), the value of 6 inexactly calculated by use of the linear correction (eq 4)will be -499.87% instead of -500.00%0,an error of only 0.13%. This difference is so small that the superior ability of cointinuous analog correction to deal wth fluctuations in I may be of little practical importance.
830
ANALYTICAL CHEMISTRY, VOL. 55, NO. 6, MAY 1983
Double Comparison. Terwilliger (6)has proposed (but not demonstrated) a system incorporating two reference gases in addition to the unknown gas. In this method, all three mass 2 ion currents are to be made precisely identical, the isotopc composition of the unknown then being calculated from
u = (A - B)[(Ru - RB)/(RA - RB)] + B
I
I
(19)
Unfortunately, burying K does not kill it. In practice, it is necessary to incorporate terms representing mismatching of mass 2 ion currents. This equation takes the form
where AB = i2,B - i 2 , A and Au = i2,u - i2,A. An exploration of the characteristics of the double-comparison technique can be based on eq 20 and on the propagation of errors associated with its terms. If the matching of mass 2 ion currents between all three samples is imperfect (Le., if the A values are nonzero), systematic errors in the determination of U will arise if its value is calculated with eq 19. The magnitude of errors of this kind can be determined by examining differences between apparent U values calculated by using eq 19 and true U values calculated by using eq 20. The result obtained is
If standards A and B differ by 500%0,under the conditions of Table I this equation reduces to Uapparent
- u t r u e ez (1.9
+
X 1 0 1 l ) ( A ~ AB)
(22)
for U values expressed in parts per mil and A values expressed in amperes. If, for example, the error is required to be less then Au AB must be less than 5.2 X lo-', A. than 1%0, Because the standard iz value has been set at 1.5 X A, this corresponds to a total mismatching of less than 0.35%. If the double-comparison method is used in combination with either a mathematical or an electrical correction, expected levels of precision can be calculated by examination of the propagation of errors in eq 20. Treating the A terms as constants, we write
+
If, for example, it is assumed that OK = 6000 A-l (10% relative standard deviation), that Au = AB = 1.5 X A (1% relative standard deviation), and that GsMOwA= 0 and 6sMowB= -500, then the predicted value of uu is everywhere less than 1%0, ranging from -0.2% near 6 = 0 to -O.i'%o near 6 = -500. If uK is improved to 600 A-l (1% relative standard deviation),
Flgure 2. Hydrogen isotope ratlo mass spectrometer equipped wlth a triple viscous leak inlet and electrical H,+ compensation circuit. The mass spectrometer is interfaced to a minicomputer (C): HV = high voltage power supply; DIA = digital to analog converter; X2 = squaring operational amplifler.
uu is essentially independent of 6, ranging only from -0.2%0 near 6 = 0 to -0.3% near 6 = -500.
EXPERIMENTAL SECTION H2 Samples. Six lecture bottles of pressurized H2 gas were generously prepared by T. C. Hoering (GeophysicalLaboratory, Carnegie Institute of Washington). Small amounts of D20 were added to a natural water sample and H, gas was produced by electrolysis. Varying proportions of the enriched gas were mixed with natural abundance Hz gas to yield D abundances between -184 to +193%0w. SMOW. For the measurements described here, an aliquot of each gas was dried by passage through a -196 O C trap and transferred to a 250-mL glass sample bulb at 1000 torr. These aliquots were used throughout the 2-month analysis period in order to provide Hz samples of constant isotopic abundance. Gas samples A and B were designated as secondary standards and were calibrated against SMOW by a series of conventional, single-comparison measurements. The SMOW standards were L over uranium converted to H2 gas by reduction of ~ - Gvolumes turnings at 800 "C (12). Repeated preparations and measurements yielded 6sMowA= 54.4 & 0.7%0(standard error, n = 8) and GsMowB = -148.1 & 0.7%0(standard error, n = 6). Instrumentation. A Nuclide 3-60 (3411. radius, 60° magnetic sector) isotope ratio mass Spectrometer with a Nier-type ion source was used for the isotopic analysis. The accelerating voltage and magnet field strength were 3300 V and 1600 G, respectively. The mass 2 and 3 ion beams were collected in individual Faraday cups connected to current-follower electrometers with 1 X 1O1O and 5 X 1011 R feedback resistors, respectively (Figure 2). The electrometer outputs were attenuated to 5 V prior t o voltage-tofrequency conversion. The output of each voltage-to-frequency converter was accumulated in a 24-bit counter. An H,+-compensation circuit was placed between the mass 2 electrometer and mass 3 electrometer (Figure 2). The circuit consisted of a variable-gain inverting amplifier and a squaring amplifier that permitted the selection of a signal equal to the H3+current, but of opposite polarity. The inlet consisted of three mercury-filled glass displacement pistons connected to three sets of switching valves via 100 cm X 0.015 cm i.d. viscous leaks. The height of the mercury column in each piston could be changed individually under computer control. An H2-gas-fluxsubroutine adjusted the height of each mercury column to produce a signal from the major ion current of 5 f 0.005 V. Procedure. Aliquots of the two working reference gases were introduced into two of the inlet reservoirs at 70 torr, producing A. The four remaining gases a mass 2 ion current of 1.5 X were introduced into the remaining inlet reservoir in randomized order. Each "unknown" was isotopically analyzed with manual and computer-controlled major ion signal matching. For manual matching, the operator adjusted the height of the mercury column until the major ion current signal was 5 k 0.05 V. After matching, the ratios of the unknown and reference sets of gas were determined 10 times and averaged. The total integration time for each gas was 100 s. The "unknown" gases were analyzed on five occasions over a 6-week period. The potentiometer controlling the
ANALYTICAL CHEMISTRY, VOL. 55, NO. 6, MAY 1983 I _ -
Table IIE. Influence of Major-Ion-Current Mismatching on the Precision of Double-Comparison Analyses Uncorrected for Ha’Formationa OS,
Z=9x Ob-
S SMQW,
oleo served
192.8 -4.9 -67.8 -1.83.6 a
6.4 2.7 4.4 10.6
i, = 1.5 X lo-’ A.
io-la
A
predicted 4.9 3.7 4.6 6.3
n = 3.
Table IV. Precision of Single- and DoubleComparison Analyses Incorporating Analog Correction for : H Formation
“lo 0
56 I
iY= 7.5 x 10-13 A -
double comparison
ob?reservedC dicted 0.6 1.9 0.4 1.4 0.8 0.5 1.7
obS SMQW,
192.8 -4.9 -67.8 -183.6
0.7
n = R2.
P P I _
electrical H3+ compensation was adjusted each day until the observed ion-current ratio was independent of H2pressure. The H3+compensation, as read from the potentiometer setting, varied with a standard deviation equivalent to 1.2 X 103/A, OF 1.7% of the typical H3+ formation constant. Calculatione. Corrections for valve leakage, mass spectrometric background, or memory were not performed as these corrections were less than 0.1%0for the range of isotopic abundances encountered. The single- and double-comparison results were calculated, in effect, using eq 13 and 20, respectively, the operations involving K being carried out in the analog domain, using the circuit shown in Figure 2. Reference gas B was used as the reference for the single comparison. The differences between mean isotopic abundances were statistically compared using the Student t test. The F test, or variance ratio test, was employed for the statistical comparison of precision as given by the standard deviations of replicate analyses.
RISSULTS AND DISCUSSION The precision of the double-comparison technique without an independent H3+correction was, as predicted, very sensitive to mismatching of the major ion intensities (Table 111). When the major ion currents were matched under computer control, with a precision of 0.05%, the standard deviations of the repeated isotope ratio determinations ranged from 0.8 to 1.9’360. For the same gases matched in the manual mode with a relative precision of 0.6%,the standard deviations ranged from 2.7 to 10.6%0.The observed standard deviations were in good agreement with the values predicted using eq 23 and 24 for the typical operating conditions of the Indiana University system (Table I). When isotopic analyses were performed in combination with electrical H3+compensation, the influence of major-ion-current mismatching on the precision of the double-comparison technique was eliminated and the precision was superior to that obtained by the single-comparison technique (Table IV). The standard deviations of the replicate analyses performed with manual intensity matching were not significantly different from those observed when computer-controlled matching was employed, The two data sets were therefore combined, and only one mean and standard deviation was calculated. The precisions of the single-comparison technique were similar to the values predicted by eq 16 and shown in Figure 1. The precision was worst when the isotopic abundance of the “unknownn was very different from that of the reference, and best when it was similar to that of the reference. The precisions of the double-comparison technique were very good, averaging 0.4%0(Table IV), but were still slightly worse than the precisions predicted for three of the four “unknown” gases.
CONCLUSIONS T e M g e r suggested that the double-comparison technique for hydrogen isotope analysis would eliminate the need for an independent H3+correction (7). Unfortunately, the dou-
O/Oo
a
serveda 0.4 0.3 0.3 0.6
predicted 0.4 0.2 0.2 0.3
831
-
0100
single comparison observeda
predicted
1.6 0.8 0.5 0.6
1.8 0.8 0.5 0.5
n = 15.
ble-comparison technique performed without independent H3+ correction is very sensitive to differences in the major ion intensity for the two reference gases and the unknown. This sensitivity to intensity mismatching results from the srnall differences in the H3+contribution to the measured ratio of each gas. For the method to provide maximum precision, the ion intensities must be matched with a relative precisioin of 0.01%, which is quite unrealistic. Even when a closed-loop computer program-controlled matching was employed, a relative matching of only 0.05% could be obtained, and even this small mismatch resulted in a significant worsening of the precision of the isotopic measurement. When the double-standard technique is used in conjunction with electrical H3+ compensation, the problem of intensity mismatching is reduced. In the present study, a precision of 0.4% was obtained, which was 2-4 times better than that of the single-comparison technique. This level of performance was obtained under conditions of normal precision in the major-ion-current matching and H3+ correction, 1 and 3%, respectively. Thus, small day-to-day variations in the lH3+ formation that probably occur as a function of source temperature and focusing, and reduce the precision of the i3ingle-comparison technique, have no significant effect on the double-comparison technique. The single-comparison technique is soundly based and can yield results of high quality. While it is susceptible to l / f noise, errors can be minimized if care is taken (i) to avoid inaccuracies in the determination of K , (ii) to stabilize the value of K between determinations of its value, and (iii) to minimize the value of K so that any residual inaccuracien or variations are of minimal effect. A problem can arise if these rather severe requirements are not met. In that case, inaccurate H+corrections can cause errors that will not be detected within the course of a normal, single-comparison measurement. This difficulty can be illustrated by a recently reported interlaboratory comparison in which standard deviations of 1.4, 2.8, and 6.6% were reported for standards that were -47, -183, and -427%0relative to SMOW (13). This pattern of increasing standard deviations with increasing isotope difference frlom the standard is indicative of 5 % errors in the H3+correction factor. Postanalysis normalization to a second standard improved the precision. An integral double-comparison analysis can provide even greater precision.
ACKNOWLEDGMENT The computer-controlled triple inlet was constructed in the chemistry department shops at Indiana University, and we are grateful for the assistance of their staffs. Laboratory assistance was provided by G. Pauly and S. A. Studley and the hydrogen gas standards were prepared in the Geophysical Laboratories of the Carnegie Institution of Washington by T. C. Hoering. Registry No. Hydrogen, 1333-74-0; deuterium, 7782-39-0.
Anal. Chem. 1083, 5 5 , 832-835
LITERATURE CITED
( I O ) Schoelier, D . A.; Hayes, J. M. Anal. Chem. 1975, 47, 408. (1 1) Peterson, D . W.; Hayes, J. M. “Contemporary Topics In Analytical and Cllnical Chemistry”; Hercules, D. M., Hieftje, Q. M., Snyder, L. R., Eds.; Plenum: New York, 1978; Vol. 3, p 217. (12) Blgeleisen, J.; Perlman, M. L.; Prosser, H. C. Anal. Chem. 1952, 2 4 , 878. (13) Qonfiantlni, R. Nature (London) 1978, 277, 534.
Nier, A. 0. Rev. Scl. Insfrum. 1947, 78, 398. McKlnney, C. R.; McCrea, J. M.; Epstein, S.; Allen, H. A.; Urcy, H. C. Rev. Sci. Instrum. 1950, 2 f , 724. Friedman, 1. Geochlm. Cosmochim. Acta 1953, 4, 89. Brldger, N. I.; Craig, R. D.; Sercombe, J. S. F. Adv. Mass Spectrom. 1974, 6, 365. Fisher, I . P.; Brown, W. F. Inf. J. Mass Specfrom. I o n fhys. 1971, 7 , 273. Terwllliger. D.T. Int. J. Mass Spectrom. Ion fhys. 1977, 25, 393. Hagemann, R.; Nlef, G.; Roth, E. Report CEA-R-3633, C.E.N. Saclay, France, 1988. Barnes, I . L.; Moore, L. J.; Machlan, L. A.; Murphy, T. J.; Shields, W. R. J. Res. Nat. Bur. Stand., Sect. A 1975, 79, 727. (9) Hagemann, R.; Nlef, G.; Roth, E. Tellus 1970, 2 3 , 712.
RECEIVED for review September 27,1982. Accepted January 21,1983. D.A. Schoeller Was suppotted by N.1.H. Grants AM 26678 and AM 30031. D. W. Petersonand the hydrogenisotope-ratio measurement system at Indiana University were supported by N.I.H. Grant GM 18979.
Calculation of Relative Electron Impact Total Ionization Cross Sections for Organic Molecules Wllllam L. Fltch” Zoecon Corporation, 975 California Avenue, Palo Alto, California 94305
Andrew D. Sauter Environmental Monltorlng Systems Laboratory,
U.S. Environmental Protection Agency, Las Vegas, Nevada 89 114
A scheme Is presented for the calculation of electron Impact total lonlzatlon ratios for organic molecules. The scheme Is based on the addltlvlty of atomic lonlzatlon cross sections. The coefflcients for the calculation are determlned by a linear regression uslng 179 total ionization cross section measurements taken from the Ilterature. The average error In the predlctlon of relative total lonlzatlon cross section for the 179 molecules was 4.69 % by this approach. Other approaches employlng dlamagnetlc susceptlbllity and molecular volume are shown to be inferior to the atomic addltlvlty scheme.
Gas chromatography/mass spectrometry (GC/MS) is the method of choice for the determination of multiple organic compounds in complex mixtures. Recent improvements in capillary gas chromatography have increased the qualitative reliability of results from analysis of environmental and clinical samples ( I , 2). Attempts to establish accuracy criteria and better define the quantitative reliability of GC/MS data led to the study of the interlaboratory reproducibility of GC/MS relative response ratios (response factors) (3). A model proposed for the prediction of response factors has been presented elsewhere (4). This model includes a chemical sensitivity term which presumes that only the total ionization cross sections of the molecules are important in adjusting their total ion current differences. Since few total ionization cross section values are available in the literature, a method to predict total ionization cross sections was required. Equation 1 has been shown to be valid for a large variety of molecules over a large range of pressures (5-10). In this It = Q I e d N (1) equation It is the total ion current, Ie is the ionizing electron current, Q is the total ionization cross section, d is the ionizing path length, and N is the concentration of molecules. Measurement of ion current as a function of pressure allows the calculation of relative total ionization cross sections. Such measurements have been made on a number of organic molecules (4-14). 0003-2700/83/0355-0832$01.50/0
Otvos and Stevenson (5) first proposed a method of calculating molecular cross sections by summing calculated atomic cross sections. Although later measurements showed this calculation scheme to be of limited applicability (6,8, 9), the Otvos and Stevenson method has been used in the literature to calculate relative sensitivity ratios in organic mass spectrometry (15,16). Harrison et al. (8), in comparing the work concluded of Otvos and Stevenson to that of Franklin et al. (6), that no simple model fits all of the data but did observe that within a homologous series of compounds a modified additivity rule applied. To explain differences between the total ionization cross sections of saturated and unsaturated molecules, Harrison noted that for electron impact ionization of the latter, there was an increased tendency toward neutral dissociation. The additivity principle of Otvos and Stevenson suffers as it does not consider these effects and other structure specific mass spectral phenomena such as doubly charged ions in the spectra of polynuclear aromatic hydrocarbons. Other molecular properties have been correlated to electron impact ionization cross section including polarizability, diamagnetic susceptibility, and molecular volume (6,8,9,17,18). None of these molecular properties is easily measured. All of the above mentioned correlations rely on the calculation of the independent variable using some form of an atomic or bond additivity principle. In an attempt to predict total ionization cross sections, we have conducted a multiple linear regression analysis between electron impact total ionization cross sections reported in the literature and atomic composition. This approach is briefly contrasted to the correlation of cross sections to molecular volume and diamagnetic susceptibility. EXPERIMENTAL SECTION Data Set. Cross sections for electron impact ionization measured at either 70 or 75 eV in a variety of different mass spectrometers were taken from the literature. As the measurement method yields relative cross sections, each literature group reported values related to a standard-usually argon or krypton. As each report included a value of cross section for n-hexane, this compound was chosen to normalize all of the data sets. Table I lists the four major literature reports from which data were taken. 0 1983 American Chemical Society
